To fail at something in such a manner that it is on an epic scale. An epic fail is typically so tragic or humiliating, it may actually be seen as funny to spectators of the event. Typically, the person or persons who took part in or caused the epic fail do not find such hilarity in their failed endeavor so easily. Pwnd is often an accurate word to describe such failure, but is not always a good word for the situation.

Tom: Man, did you see that kid who tried to climb that fence over there? He slipped and got a major wedgie!

Jerry: Dude! That is such an epic fail!

or

Harry: I can't believe I just embarrassed myself in front of all those people by tripping and falling off the stage during my lecture on fruitbats today...